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One can specify the following mathematical characteristics in each of the five Platonic solids:
1. The radius of the sphere circumscribing the polyhedron;
2. The radius of the sphere inscribed in the polyhedron;
3. The surface area of the polyhedron;
4. The volume of the polyhedron.
A polyhedron is a solid bounded by flat polygons, which are called faces. The sides of the faces are called edges, and their corners are called vertices. Depending on the number of faces one can specify a tetrahedron (4 faces), pentahedron (5 faces), etc. A polyhedron is considered to be convex if it is located on one side of the plane of each of its faces. A polyhedron is called regular if its faces are regular polygons (i.e., where all sides and angles are equal) and all polyhedral angles at the vertices are equal. There are five types of regular polyhedra: tetrahedron, cube (regular hexahedron), octahedron, dodecahedron, icosahedron.
Studio Artemy Lebedev (makes the design for the leading search engine Yandex) was proposed form of a birdhouse in the form of a polyhedron.
The correct polyhedron, the icosahedron, was chosen as the geometric shape.